Function Operations & Inverses
Exponential Functions
Logarithmic Functions
Natural Log
100
Which of these graphs represent one-to-one functions.
B & D
100
For the exponential function y = 150(1.15)t, identify the initial population and the percent change and state whether the function models exponential growth or exponential decay.
1; 115%; growth
100
Evaluate log2128
7
100
Which of the following are true statements? List all correct answers.
a. ln e = 1
b. log30 = 1
c. log (x + y) = log x + log y
d. logbar = r logba
e. logbx = (ln x)/(ln b)
A, D, E
200
Evaluate
(g@f)(3)
1
200
What is the asymptote of
y=3^(x+2)-1?
y=-1
200
Which of the following are increasing functions? List all correct answers.
a. y = 3x
b. y = log3x
c. y = log1/2x
d. y = (1/2)x
e. y = 3–x
A, B
200
Solve
e^(ln(x^2-3))=1
2
300
Find the rule for the inverse of
f(x)=(3x+2)/(2x-1)
f^-1(x)=(x+2)/(2x-3)
300
Which of the following are decreasing functions? List all correct answers.
a. f(x) = 2x c. f(x) = 0.5x
b. f(x) = –3x d. f(x) = 1x
B, C
300
Solve log (x + 15) + log(x + 1) = 0.5 log 4 + log 3 + log (3x + 5).
x = 5
300
Juan plans to retire in 20 yr. How much money does he need to invest now at 5% APR compounded quarterly if he will need $250,000 when he retires?
$92,541.70
400
A store is going out of business. The first week it marks down every item 25% and then advertises an additional 20% off the marked-down price. The next week it advertises 40% off the original price. If x is an item's original price, write simplified expressions for the item's price during the first and the second week of the sale.
first week: 0.6x
second week: 0.6x
400
Which of the following functions are decay functions? List all correct answers.
a. y = 2(1 – 0.05) t
b. y = 0.5(0.75)t
c. y = 3(1 + 0.025)t
d. y = 0.2(1.3)t
e. y = – 7(1)t
A, B
400
Solve 7.2y + 7.2 = 33.4 for y. Round your answer to the nearest hundredth.
1.65
400
Would it be better to invest at 6% APR compounded annually or 5.8% APR compounded continuously?
Anually
500
Consider the graph of f(x) = a(b)x + c.
a. Determine the value of c.
b. Use the x-intercept to determine the value of a.
c. Use another point on the graph to determine the value of b.
c= -3
a = 3
b = 2
500
According to current estimates, the population of an endangered species is about 400 and is decreasing by 10% each year. Write an exponential function to model the future population. Use the model to predict the population after 10 yr.
P(t) = 400(0.9)t ; P(10) = 139
500
If L1 and L2 are the amounts of light received from two stars, and m1 and m2 are the apparent magnitudes of the stars, then m1 - m2 = -2.5 log (L1/L2). If the difference m1 - m2, how many times more light do we receive from the second star? (Brightness is measured in apparent magnitude because a brighter star may appear fainter if it is farther away.)
6.3
500
Solve 7x+3 = 27x+2. Round your answer to the nearest ten thousandth.
-0.559